Jet Propulsion Laboratory Development Ephemeris (abbreviatedJPL DE(number), or simplyDE(number)) designates one of a series of mathematicalmodels of theSolar System produced at theJet Propulsion Laboratory inPasadena, California, for use in spacecraft navigation and astronomy. The models consist of numeric representations ofpositions,velocities andaccelerations of major Solar System bodies, tabulated at equally spaced intervals of time, covering a specified span of years.[1]Barycentricrectangular coordinates of theSun, eight majorplanets andPluto, and geocentric coordinates of theMoon are tabulated.
There have been many versions of theJPL DE, from the 1960s through the present,[2] in support of both robotic and crewed[3] spacecraft missions. Available documentation is limited, but we knowDE69 was announced in 1969 to be the third release of the JPL Ephemeris Tapes, and was a special purpose, short-duration ephemeris. The then-current JPL Export Ephemeris wasDE19. These early releases were distributed onmagnetic tape.
In the days before personal computers, computers were large and expensive, and numerical integrations such as these were run by large organizations with ample resources. The JPL ephemerides prior toDE405 were integrated on aUnivac mainframe indouble precision. For instance,DE102, which was created in 1977, took six million steps and ran for nine days on aUnivac 1100/81.[4]DE405 was integrated on aDEC Alpha inquadruple precision.[5]
In the 1970s and early 1980s, much work was done in the astronomical community to update the astronomical almanacs from thetheoretical work of the 1890s to modern, relativistic theory. From 1975 through 1982, six ephemerides were produced at JPL using the modern techniques of least-squares adjustment of numerically-integrated output to high precision data:DE96 in Nov. 1975,DE102 in Sep. 1977,DE111 in May 1980,DE118 in Sep. 1981, andDE200 in 1982.[6]DE102 was the first numerically integrated so-called Long Ephemeris, covering much of history for which useful astronomical observations were available: 1141 BC to AD 3001.DE200, a version ofDE118 migrated to theJ2000.0 reference frame, was adopted as thefundamental ephemeris for the new almanacs starting in 1984. DE402 introduced coordinates referred to theInternational Celestial Reference Frame (ICRF).DE440 andDE441 were published in 2021, with improvements in the orbits of Jupiter, Saturn and Pluto from more recent spacecraft observations.[7]
JPL ephemerides have been the basis of the ephemerides of sun, moon and planets in theAstronomical Almanac since the volumes for 1984 through 2002, which used JPL's ephemerisDE200. (From 2003 through 2014 the basis was updated to useDE405, and further updated from 2015 whenDE430 began to be used.)[8][9]
Eachephemeris was produced bynumerical integration of theequations of motion, starting from a set of initial conditions. Due to the precision of modern observational data, theanalytical method ofgeneral perturbations could no longer be applied to a high enough accuracy to adequately reproduce the observations. The method ofspecial perturbations was applied, using numerical integration to solve then-body problem, in effect putting the entire Solar System into motion in the computer's memory, accounting for all relevant physical laws. The initial conditions were both constants such asplanetary masses, from outside sources, and parameters such as initial positions and velocities, adjusted to produce output which was a "best fit" to a large set ofobservations. Aleast-squares technique was used to perform the fitting.[4] As of DE421, perturbations from 343 asteroids, representing about 90% of the mass of themain asteroid belt, have been included in the dynamical model.[10]
The physics modeled included the mutualNewtonian gravitational accelerations and theirrelativistic corrections (a modified form of theEinstein-Infeld-Hoffmann equations), theaccelerations caused by the tidal distortion of the Earth, the accelerations caused by thefigure of the Earth and Moon, and a model of the lunarlibrations.[4]
The observational data in the fits has been an evolving set, including: ranges (distances) to planets measured by radio signals from spacecraft,[11] directradar-ranging of planets, two-dimensional position fixes (on the plane of the sky) byVLBI of spacecraft,transit andCCD telescopic observations of planets and small bodies, andlaser-ranging ofretroreflectors on the Moon, among others.DE102, for instance, was fit to 48,479 observations.
The time argument of the JPL integrated ephemerides, in early versions known asTeph,[12] became recognized as arelativistic coordinate time scale, as is necessary in precise work to account for the smallrelativistic effects oftime dilation andsimultaneity. TheIAU's 2006 redefinition ofTDB became essentially equivalent to Teph, and the redefined TDB has been explicitly adopted in recent versions of the JPL ephemerides.
Positions and velocities of the Sun, Earth, Moon, and planets, along with the orientation of the Moon, are stored asChebyshev polynomial coefficients fit in 32 day-long segments.[10] The ephemerides are now available via World Wide Web andFTP[13] as data files containing the Chebyshev coefficients, along with source code to recover (calculate) positions and velocities.[14] Files vary in the time periods they cover, ranging from a few hundred years to several thousand, and bodies they include. Data may be based on each planet's geometric center or a planetary-systembarycenter.
The use of Chebyshev polynomials enables highly precise, efficient calculations for any given point in time.DE405 calculation for theinner planets "recovers" accuracy of about 0.001 seconds of arc (arcseconds) (equivalent to about 1 km at the distance ofMars); for theouter planets it is generally about 0.1 arcseconds. The 'reduced accuracy'DE406 ephemeris gives an interpolating precision (relative to the full ephemeris values) no worse than 25 metres for any planet and no worse than 1 metre for the Moon.
Note that these precision numbers are for the interpolated values relative to the original tabulated coordinates. The overall precision and accuracy of interpolated values for describing the actual motions of the planets will be a function of both the precision of the ephemeris tabulated coordinates and the precision of the interpolation.
Ephemerides for Solar System bodies are available through a JPL website[17] and via FTP.[18]
Source:[10]
DE440[19] was created in June 2020. The new DE440 / 441 general-purpose planetary solution includes seven additional years of ground and space-based astrometric data, data calibrations, and dynamical model improvements, most significantly involving Jupiter, Saturn, Pluto, and the Kuiper Belt. Inclusion of 30 new Kuiper-belt masses, and the Kuiper Belt ring mass, results in a time-varying shift of ~100 km in DE440'sbarycenter relative to DE430. The 114 Megabyte ephemeris files include the orientation of the Moon. It spans the years 1550–2650. JPL started transitioning to DE440 in early April 2021. Supplemental versions are also available which include the planetary geometric center of Mars as well as Mars' barycenter.[20]
DE441[19] was created in June 2020. This ephemeris is longer than DE440, -13,200 to 17,191, but less accurate (due to neglecting lunar core-mantle damping). It is useful for analyzing historical observations that are outside the span of DE440.
DE102 was created in 1981; includes nutations but not librations. Referred to the dynamical equator and equinox of 1950. Covers early 1410 BC through late 3002 AD.[14]
DE200 was created in 1981; includes nutations but not librations. Referred to the dynamical equator and equinox of 2000. Covers late 1599 AD through early 2169 AD. This ephemeris was used for theAstronomical Almanac from 1984 to 2003.[14]
DE202 was created in 1987; includes nutations and librations. Referred to the dynamical equator and equinox of 2000. Covers late 1899 through 2049.[14]
DE402 was released in 1995, and was quickly superseded by DE403.
DE403[21] was created 1993, released in 1995, expressed in the coordinates of theInternational Earth Rotation Service (IERS) reference frame, essentially the ICRF. The data compiled by JPL to derive the ephemeris began to move away from limited-accuracy telescopic observations and more toward higher-accuracyradar-ranging of the planets, radio-ranging of spacecraft, andvery-long-baseline-interferometric (VLBI) observations of spacecraft, especially for the four inner planets. Telescopic observations remained important for the outer planets because of their distance, hence the inability to bounce radar off of them, and the difficulty of parking a spacecraft near them. Theperturbations of 300 asteroids were included, vs DE118/DE200 which included only the five asteroids determined to cause the largest perturbations. Better values of the planets' masses had been found since DE118/DE200, further refining the perturbations.Lunar Laser Ranging accuracy was improved, giving better positions of the Moon. DE403 covered the time span early 1599 to mid 2199.[22]
DE404[23] was released in 1996. A so-called Long Ephemeris, this condensed version of DE403 covered 3000 BC to AD 3000. While both DE403 and DE404 were integrated over the same timespan, the interpolation of DE404 was somewhat reduced in accuracy andnutation of the Earth andlibration of the Moon were not included.
DE405[24] was released in 1998. It added several years' extra data from telescopic, radar, spacecraft, and VLBI observations (of theGalileo spacecraft at Jupiter, in particular). The method of modeling the asteroids' perturbations was improved, although the same number of asteroids were modeled. The ephemeris was more accurately oriented onto the ICRF. DE405 covered 1600 to 2200 to full precision. This ephemeris was utilized in theAstronomical Almanac from 2003 until 2014.
DE406 was released with DE405 in 1998. A Long Ephemeris, this was the condensed version of DE405, covering 3000 BC to AD 3000 with the same limitations as DE404. This is the same integration as DE405, with the accuracy of the interpolating polynomials has been lessened to reduce file size for the longer time span covered by the file.
DE407[25] was apparently unreleased. Details in readily-available sources are sketchy.
DE408[26] was an unreleased ephemeris, created in 2005 as a longer version of DE406, covering 20,000 years.
DE409[27] was released in 2003 for theMars Exploration Rover spacecraft arrival at Mars and theCassini arrival at Saturn. Further spacecraft ranging and VLBI (to theMars Global Surveyor,Mars Pathfinder and theMars Odyssey spacecraft) and telescopic data were included in the fit. The orbits of thePioneer andVoyager spacecraft were reprocessed to give data points for Saturn. These resulted in improvements over DE405, especially to the predicted positions of Mars and Saturn. DE409 covered the years 1901 to 2019.
DE410[28] was also released in 2003 covered 1901 - 2019, with improvements from DE409 in the masses for Venus, Mars, Jupiter, Saturn and the Earth-Moon system based on recent research. Though the masses had not yet been adopted by theIAU. The ephemerides were created to support the arrivals of theMER andCassini spacecraft.
DE411[29] was widely cited in the astronomical community, but not publicly released by JPL
DE412[30] was widely cited in the astronomical community, but not publicly released by JPL
DE413[29] was released in 2004 with updated ephemeris ofPluto in support of theoccultation of a star by its satelliteCharon on 11 Jul 2005. DE413 was fit to newCCD telescopic observations of Pluto in order to give improved positions of the planet and its moon.
DE414[31] was created in 2005 and released in 2006. Thenumerical integration software was updated to usequadruple-precision for theNewtonian part of theequations of motion. Ranging data to theMars Global Surveyor andMars Odyssey spacecraft were extended to 2005, and further CCD observations of the five outer planets were included in the fit. Some data was accidentally left out of the fit, namelyMagellan Venus data for 1992-94 and Galileo Jupiter data for 1996-97. Some ranging data to theNEAR Shoemaker spacecraft orbiting the asteroidEros was used to derive the Earth/Moon mass ratio. DE414 covered the years 1599 to 2201.
DE418[32] was released in 2007 for planning theNew Horizons mission to Pluto. New observations of Pluto, which took advantage of the newastrometric accuracy of theHipparcos star catalog, were included in the fit. Mars spacecraft ranging and VLBI observations were updated through 2007. Asteroid masses were estimated differently. Lunar laser ranging data for the Moon was added for the first time since DE403, significantly improving the lunar orbit and librations. Estimated position data from theCassini spacecraft was included in the fit, improving the orbit of Saturn, but rigorous analysis of the data was deferred to a later date. DE418 covered the years 1899 to 2051, and JPL recommended not using it outside of that range due to minor inconsistencies which remained in the planets' masses due to time constraints.
DE421[33] was released in 2008. It included additional ranging and VLBI measurements of Mars spacecraft, new ranging and VLBI of theVenus Express spacecraft, the latest estimates of planetary masses, additional lunar laser ranging, and two more months of CCD measurements of Pluto. When initially released in 2008, the DE421 ephemeris covered the years 1900 to 2050. An additional data release in 2013 extended the coverage to the year 2200.
DE422[34] was created in 2009 for theMESSENGER mission to Mercury. A Long Ephemeris, it was intended to replace DE406, covering 3000 BC to AD 3000.
DE423[35] was released in 2010. Position estimates of theMESSENGER spacecraft and additional range and VLBI data from the Venus Express spacecraft were fit. DE423 covered the years 1799 to 2200.
DE424[36] was created in 2011 to support theMars Science Laboratory mission.
DE430[37] was created in 2013 and Is intended for use in analyzing modern data. It covers the dates 1550 January 1 to 2650 January 22 with the most accurate lunar ephemeris. From 2015 onwards this ephemeris is utilized in theAstronomical Almanac. Beginning with this release only Mars' Barycenter was included due to the small masses of its moons Phobos and Deimos which create a very small offset from the planet's center.[38] The complete ephemerides files is 128 megabytes but several alternative versions have been made available by JPL[10]
DE431[37] was created in 2013 and is intended for analysis of earlier historical observations of the Sun, Moon, and planets. It covers a longer time span than DE430 (13201 BC to AD 17191) agreeing with DE430 within 1 meter over the time period covered by DE430. Position of the Moon is accurate within 20 meters between 1913-2113 and that error grows quadratically outside of that range.[39] It is the largest of the ephemerides files at 3.4 gigabytes.[40]
DE432[41] was created April 2014. It includes librations but no nutations. DE432 is a minor update to DE430, and is intended primarily to aid the New Horizons project targeting of Pluto.[42]
DE436[43] was created in 2016 and was based on the DE430, with improved orbital data for Jupiter specifically for theJuno mission).
DE438[44] was created in 2018 and was based on the DE430, with improved orbital data for Mercury (for theMESSENGER mission), Mars (for theMars Odyssey andMars Reconnaissance Orbiters), and Jupiter (forJuno).